AI 中文总结
本文以耦合混沌踢玻色-哈伯德系统为研究对象，结合对称性分辨纠缠与量子混沌微扰理论，揭示了二分多体系统中由对称性破缺引发的普适纠缠相变及本征态局域化特性。
AI 中文摘要
我们研究二分多体系统中的平均本征态纠缠，该系统表现出两个局域守恒律破缺为一个全局守恒量的特性，玻色-哈伯德系统中的粒子数守恒可实现该设定。我们设计了对应的随机矩阵模型，其捕捉了该对称性破缺的普适特征，可应用强大的随机矩阵方法。结合对称性分辨纠缠概念与量子混沌系统的微扰理论，我们得到了依赖单个基本参数的普适纠缠相变。此外，对称性分辨纠缠可将真实纠缠与源自守恒量的部分分离，后者由数熵量化。研究表明，对称性破缺因时间演化算子的带状结构会导致本征态局域化，通过将结果外推至微扰区域之外，我们得到了完整相变的解析描述。
英文摘要
We investigate the average eigenstate entanglement in a bipartite many-body system which exhibits a breaking of two local conservation laws into a global conserved quantity. Such a setting is realized by the particle number conservation in Bose-Hubbard systems. We devise a corresponding random matrix model which captures the universal features of this symmetry breaking and allows for applying powerful random matrix methods. By combining the concept of symmetry resolved entanglement with perturbation theory for quantum chaotic systems we obtain a universal entanglement transition depending on a single fundamental parameter. Furthermore, the symmetry resolved entanglement allows for separating the genuine entanglement from the part which originates from the conserved quantity. This latter contribution is quantified by the number entropy. For this it is shown that the symmetry breaking generates a localization of the eigenstates due to a banded structure of the time-evolution operator. By extrapolating the results beyond the perturbative regime we obtain an analytic description of the full transition.
